3,208 research outputs found
Weak-Strong uniqueness for compressible Navier-Stokes system with degenerate viscosity coefficient and vacuum in one dimension
We prove weak-strong uniqueness results for the compressible Navier-Stokes
system with degenerate viscosity coefficient and with vacuum in one dimension.
In other words, we give conditions on the weak solution constructed in
\cite{Jiu} so that it is unique. The novelty consists in dealing with initial
density which contains vacuum. To do this we use the notion of
relative entropy developed recently by Germain, Feireisl et al and Mellet and
Vasseur (see \cite{PG,Fei,15}) combined with a new formulation of the
compressible system (\cite{cras,CPAM,CPAM1,para}) (more precisely we introduce
a new effective velocity which makes the system parabolic on the density and
hyperbolic on this velocity).Comment: arXiv admin note: text overlap with arXiv:1411.550
Global strong solutions to the planar compressible magnetohydrodynamic equations with large initial data and vaccum
This paper considers the initial boundary problem to the planar compressible
magnetohydrodynamic equations with large initial data and vacuum. The global
existence and uniqueness of large strong solutions are established when the
heat conductivity coefficient satisfies \begin{equation*}
C_{1}(1+\theta^q)\leq \kappa(\theta)\leq C_2(1+\theta^q) \end{equation*} for
some constants , and .Comment: 19pages,some typos are correcte
Relative entropy for compressible Navier-Stokes equations with density dependent viscosities and applications
Recently, A. Vasseur and C. Yu have proved the existence of global
entropy-weak solutions to the compressible Navier-Stokes equations with
viscosities and and a pressure
law under the form with and
constants. In this note, we propose a non-trivial relative entropy for such
system in a periodic box and give some applications. This extends, in some
sense, results with constant viscosities initiated by E. Feiersl, B.J. Jin and
A. Novotny.
We present some mathematical results related to the weak-strong uniqueness,
convergence to a dissipative solution of compressible or incompressible Euler
equations. As a by-product, this mathematically justifies the convergence of
solutions of a viscous shallow water system to solutions of the inviscid
shall-water system
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